复杂结构的Beltrami参数化在二维自由共形场论中的作用
The role of the Beltrami parametrization of complex structures in 2-d Free Conformal Field Theory
摘要：
本讲座回顾了复几何和2维共形场论的拉格朗日公式是如何紧密联系在一起的。特别是，如何使用Beltrami参数化的复杂结构的紧凑的黎曼曲面完全符合著名的局部性原则的场论，后者需要使用无限维空间。它还允许直接应用的局部指数定理的家庭椭圆算子由于J. - M. Bismut，H. Gillet和C.苏雷在自由自旋$j$ b-c系统或更一般的紧致黎曼曲面上具有全纯向量丛的值截面的自由场的情况下，将讨论配备有Quillenburn度量的行列式线丛与所谓的全纯因式分解性质之间的联系。
英文摘要：
This talk gives a review on how complex geometry and a Lagrangian formulation of 2-d conformal field theory are deeply related. In particular, how the use of the Beltrami parametrization of complex structures on a compact Riemann surface fits perfectly with the celebrated locality principle of field theory, the latter requiring the use infinite dimensional spaces. It also allows a direct application of the local index theorem for families of elliptic operators due to J.-M. Bismut, H. Gillet and C. Soulé. The link between determinant line bundles equipped with the Quillenś metric and the so-called holomorphic factorization property will be addressed in the case of free spin $j$ b-c systems or more generally of free fields with values sections of a holomorphic vector bundles over a compact Riemann surface.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
